JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III DYNAMICS OF MACHINERY Previous Question Paper (August - 2022 - R13)
Answer any five questions. All questions carry equal marks.
Main
Derive an expression for the gyroscopic couple acting on a disc of moment of inertia I, rotating with speed ω and speed of precession ωp.
Answer
Consider a disc of moment of inertia I rotating with an angular velocity ω about its axis of spin. Let the axis of spin be precessing about a perpendicular axis with an angular velocity ωp. The angular momentum of the disc is L = Iω, represented as a vector along the axis of spin. Due to the precession of the axis, the change in angular momentum dL in a small time dt is given by dL = L × ωp × dt. The gyroscopic couple C is the rate of change of angular momentum:
The direction of the couple is determined by the right-hand rule, acting in a plane perpendicular to both the axis of spin and the axis of precession.
An aeroplane makes a complete half circle of 60 m radius towards the left when flying at 180 km/h. The rotary engine and the propeller of the plane have a mass of 35 kg with radius of gyration of 0.25 m. The engine runs at 2400 rpm cw, when viewed from the rear. Find the gyroscopic couple on the plane and state its effect on it. What will be the effect if the aeroplane turns to its right instead of the left?
Answer
Given: Velocity v = 180 km/h = 50 m/s, radius R = 60 m, mass m = 35 kg, radius of gyration k = 0.25 m, speed N = 2400 rpm.
1. Calculate angular velocity of spin ω:
2. Calculate moment of inertia I:
3. Calculate angular velocity of precession ωp:
4. Calculate gyroscopic couple C:
Effect of left turn: Since the propeller rotates clockwise (viewed from rear) and turns left, the gyroscopic couple acts to lift the nose of the aeroplane. Effect of right turn: If the aeroplane turns to the right, the direction of the gyroscopic couple reverses, causing the nose of the aeroplane to dip downwards.
Explain the concept of equivalent offset inertial force with reference to mechanisms.
Answer
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In a four-bar mechanism the dimensions of the various links with AD as fixed link are given by AB = CD = 200 mm, BC = 300 mm and AD = 400 mm. At the midpoint on the link CD a force of 3 kN act perpendicular to the link. Calculate the input torque to link AB for the static equilibrium of the mechanism.
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Differentiate between the thin-film and thick-film lubrications.
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A clutch in a motor car is of single-plate type having both sides of the plate effective. It is required to transmit 35 kW at 1500 rpm. The axial thrust is 0.75 MPa. The ratio between the external and internal radii of the plate is 1.5 and coefficient of friction is 0.25. Assuming uniform pressure, determine the dimensions of the clutch.
Answer
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Explain the prony brake dynamometer with a neat sketch. Also derive an expression for Brake power.
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A simple band brake is operated by a lever of length 500 mm. The brake drum has a diameter of 500 mm and the brake band embraces 5/8 of the circumference. One end of the band is attached to the fulcrum of the lever while the other end is attached to a pin on the lever 100 mm from the fulcrum. If the effort applied to the end of the lever is 2 kN and the coefficient of friction is 0.25, find the braking torque on the drum.
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Define coefficient of fluctuation of energy and coefficient fluctuation of speed.
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The equation of the turning moment curve of a three crank engine is (5+1.5sin 3θ) kNm, where θ is the crank angle. The moment of inertia of the flywheel is 1000 kg m2 and the mean engine speed is 300 rpm. Calculate power of the engine and the maximum fluctuation of the speed of the flywheel when the resisting torque is constant.
Answer
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How does centrifugal governor differ from an inertia governor? Explain.
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A Porter governor has all four arms 200 mm long. The upper arms are attached on the axis of rotation and the lower arms are attached to the sleeve at a distance of 25 mm from the axis. The mass of each ball is 5 kg and the mass of sleeve is 40 kg. The extreme radii of rotation are 150 mm and 200 mm. Determine the range of speed of governor. Also find the effort and power of the governor.
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Differentiate between static balancing from dynamic balancing.
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Four masses M1, M2, M3 and M4 are 200kg, 300kg, 250kg and 350kg respectively. The corresponding radii of rotation are 0.2 m, 0.25 m, 0.25 m and 0.3 m respectively and the angle between successive masses are 45, 90 and 135 degrees. Find the position and magnitude of balance mass required if its radius of rotation is 0.25m.
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Explain the concept of whirling of a shaft. Also give the suitable expression.
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Determine the natural frequency and position of the node for the free torsional vibrations of the stepped shaft shown in figure. Take shear modulus, G = 80 GPa.
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